Pinning Control Technique Research Articles

Cluster synchronization of fractional-order coupled genetic regulatory networks via pinning control

Cell-to-cell interaction and quorum sensing are universal in real life and have an extremely important biological significance. Besides, fractional-order calculus has tremendous advantages in describing the memory of neurons and the inheritance of genes. In this article, the cluster synchronization of fractional-order coupled genetic regulatory networks (GRNs) is explored by applying pinning control technique. First of all, a type of coupled fractional-order models about GRNs is proposed based on the quorum sensing and cluster expression characteristics of genes. Secondly, by designing pinning control strategies and fractional-order inequalities, several sufficient criteria are constructed to reach cluster synchronization. Furthermore, the selection rule of pining nodes is provided to conduct what nodes can be selected to be pinned and how many nodes are pinned to achieve cluster synchronization. In addition, the fractional-order adaptive control strategy is designed to regulate control gains. Several numerical results are provided lastly to confirm the theoretical analysis.

Minimal pinning control for set stability of Boolean networks

In this paper, set stability of Boolean networks (BNs) is studied based on semi-tensor product of matrices. First, an index-vector is introduced to verify whether a BN can be set stable from an initial set to a destination set. Then, an algorithm is proposed to obtain the minimal set of pinning nodes to achieve set stability, if a BN is not set stable. Moreover, in order to reduce the computational complexity, a hybrid pinning control technique is proposed, where the designed controllers are not entirely dependent on all the nodes of the networks. Further, the issue of synchronization is discussed by using the proposed hybrid pinning control methods. Finally, simulations are presented to illustrate the effectiveness of the obtained results in this paper.

Finite-time synchronization and topology identification of stochastic multi-layer networks with Markovian switching

The finite-time synchronization and topology identification problems of stochastic multi-layer networks with Markovian switching are investigated in this paper. Compared with previous studies, Markovian switching is considered in stochastic multi-layer networks. First, by using Kirchhoff’s matrix tree theorem in graph theory, the Lyapunov function of the coupling system is constructed indirectly from the Lyapunov function of the vertex system. In view of finite-time stability theory and stochastic analysis technique, some finite-time synchronization criteria of stochastic multi-layer networks are proposed. Moreover, the intra-layer and inter-layer topological structures are successfully identified in finite time. Then, using the pinning control technique, the unknown partial topological structures are also identified in finite time. In the end, two examples for whole and partial topology identification of two-layer small-world networks are given.

Bipartite synchronization for cooperative-competitive neural networks with reaction–diffusion terms via dual event-triggered mechanism

The pinning-like bipartite synchronization is investigated for reaction–diffusion neural networks with cooperative-competitive interactions in this paper. First, a dural event-triggered control algorithm based on the time–space sampled-data scheme is employed to further decrease the transmission resources’ consumption. Then, some sufficient conditions that guarantee the bipartite synchronization for the target neural networks with the signed graph are obtained by virtue of the Lyapunov method, Halanay’s inequalities, and the pinning control technique. Moreover, new weighted integral inequalities are introduced to get higher upper bounds than what traditional inequality produces. Finally, a numerical simulation result is given to validate the advantages of the proposed method for realizing bipartite synchronization.

Intermittent Cluster Consensus Control of Multiagent Systems From a Static/Dynamic Output Approach

This article is concerned with the cluster consensus control problem for multiagent linear systems with a directed communication topology, where only relative output measurements of neighboring agents are available to each agent. Motivated by the pinning control technique, both static and dynamic intermittent output control strategies are proposed. Using Lyapunov functions, sufficient conditions are developed to ensure cluster consensus with existence-guaranteed control parameters. Both periodic and nonperiodic operations of intermittent controllers are investigated. Finally, the effectiveness of the theoretical results is demonstrated by a simulation example.

Impulsive Pinning Control of Discrete-Time Complex Networks with Time-Varying Connections

Complex dynamical networks with time-varying connections have characteristics that allow a better representation of real-world complex systems, especially interest in their not static behavior and topology. Their applications reach areas such as communication systems, electrical systems, medicine, robotic, and more. Both continuous and discrete-time complex dynamical networks and the pinning control technique have been studied. However, even with interest in the research on complex networks combining characteristics of discrete-time, time-varying connections, pinning control, and impulsive control, there are few studies reported in the literature. There are some previous studies dealing with impulsively pin-controlling a discrete-time complex network. Nevertheless, they neglect to deal with time-varying connections; they deal with these systems by experimentally using continuous-time methods or linearizing the node dynamics. In this manner, this paper presents a control scheme that not only deals with pin control on discrete-time complex networks but also includes time-varying connections. This paper proposes an impulsive pin control to a zero state using passivity degrees considering a discrete-time complex network with undirected, linear, and diffusive couplings. Additionally, a corresponding mathematical analysis, which allows the representation of the dynamics as a set of symmetric matrices, is presented. With this, certain kinds of time-varying connections can be integrated into the analysis. Moreover, a particular criterion for selecting nodes to pin is also presented. The behavior of the controller for the non-varying and time-varying coupling cases is shown via numeric simulations.

Pinning bipartite synchronization for coupled reaction–diffusion neural networks with antagonistic interactions and switching topologies

In this paper, the bipartite synchronization issue for a class of coupled reaction–diffusion networks with antagonistic interactions and switching topologies is investigated. First of all, by virtue of Lyapunov functional method and pinning control technique, we obtain some sufficient conditions which can guarantee that networks with signed graph topologies realize bipartite synchronization under any initial conditions and arbitrary switching signals. Secondly, for the general switching signal and periodic switching signal, a pinning controller that can ensure bipartite synchronization of reaction–diffusions networks is designed based on the obtained conditions. Meanwhile, a directed relationship between coupling strength and control gains is presented. Thirdly, numerical simulation is provided to demonstrate the correctness and validity of the derived theoretical results for reaction–diffusion systems. We briefly conclude our findings and future work.

Scaled consensus problem for multi-agent systems with semi-Markov switching topologies: A view from the probability

This paper investigates the stochastic scaled consensus problem for multi-agent systems with semi-Markov switching topologies. Sufficient conditions are established to guarantee the addressed system to realize the scaled consensus with probability one, which means that all agents’ states almost surely reach a dictated proportion. Here, the semi-Markov process concerned is much more general than those utilized in the recent literature, which can be characterized by two important factors: (1) the transition probability matrix, and (2) the polytropical distribution functions of sojourn times. In addition, pinning scaled consensus protocol is designed by employing the pinning control technique, where only the root nodes of the union set of all the topologies are chosen to be pinned, and the final desired state value of the considered system can be realized with probability one. Finally, numerical simulations are provided to illustrate validity of the obtained main results.

Cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noises

This paper focuses on the mean square cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noise via pinning control technique. Network topology can take weaker conditions in each cluster but an extra balanced condition is also needed. A time-varying control gain will be introduced to eliminate the effect of stochastic noise. For the case of fixed topology, if the induced digraph of each cluster has a directed spanning tree, the sufficient conditions for the mean square cluster consensus can be obtained. For the case of Markovian switching topologies, if the induced digraph of union of the Laplacian matrix of each mode has a directed spanning tree, the mean square cluster consensus conclusion can be derived. Particularly, if the elements of transition probability of Markov chain are partly unknown, we can also obtain the same conclusion under the same conditions. Finally, two examples are given to illustrate our results.

Finite-time consensus for multi-agent systems with nonlinear dynamics under Euler digraph via pinning control

This paper addresses the finite-time consensus problem for multi-agent systems with nonlinear dynamics under Euler digraph. By pinning control technique, a nonlinear distributed protocol is proposed, which ensures that all the agents can be controlled to the pinner's trajectory in finite time. Furthermore, we solve the challenging and fundamental question that how many nodes should be pinned to reach finite-time consensus. A sufficient condition is proposed to achieve finite-time consensus for multi-agent systems with nonlinear dynamics under Euler digraph. It is found that adding communication connections or increasing feedback gains is an effective way to reduce the settling time. Finally, numerical simulations are presented to verify the effectiveness of the obtained theoretical results.

Pinning Control for the p53-Mdm2 Network Dynamics Regulated by p14ARF.

p53 regulates the cellular response to genotoxic damage and prevents carcinogenic events. Theoretical and experimental studies state that the p53-Mdm2 network constitutes the core module of regulatory interactions activated by cellular stress induced by a variety of signaling pathways. In this paper, a strategy to control the p53-Mdm2 network regulated by p14ARF is developed, based on the pinning control technique, which consists into applying local feedback controllers to a small number of nodes (pinned ones) in the network. Pinned nodes are selected on the basis of their importance level in a topological hierarchy, their degree of connectivity within the network, and the biological role they perform. In this paper, two cases are considered. For the first case, the oscillatory pattern under gamma-radiation is recovered; afterward, as the second case, increased expression of p53 level is taken into account. For both cases, the control law is applied to p14ARF (pinned node based on a virtual leader methodology), and overexpressed Mdm2-mediated p53 degradation condition is considered as carcinogenic initial behavior. The approach in this paper uses a computational algorithm, which opens an alternative path to understand the cellular responses to stress, doing it possible to model and control the gene regulatory network dynamics in two different biological contexts. As the main result of the proposed control technique, the two mentioned desired behaviors are obtained.

New developments in control design techniques of logical control networks

The control design problem plays a fundamental role in the study of logical control networks (LCNs). This paper presents a detailed survey on new developments in control design techniques of LCNs. First, some preliminary results on the semi-tensor product method and LCNs are reviewed. Then, we move on to some new developments for control design techniques of LCNs, including the reachable set approach, the pinning control technique, the control Lyapunov function approach, the event-triggered control technique, and the sampled-data control technique. Finally, an illustrative example is given to demonstrate the effectiveness of these techniques.

Global exponential synchronization of delayed memristive neural networks with reaction–diffusion terms

This paper investigates the global exponential synchronization problem of delayed memristive neural networks (MNNs) with reaction–diffusion terms. First, by utilizing the pinning control technique, two novel kinds of control methods are introduced to achieve synchronization of delayed MNNs with reaction–diffusion terms. Then, with the help of inequality techniques, pinning control technique, the drive–response concept and Lyapunov functional method, two sufficient conditions are obtained in the form of algebraic inequalities, which can be used for ensuring the exponential synchronization of the proposed delayed MNNs with reaction–diffusion terms. Moreover, the obtained results based on algebraic inequality complement and improve the previously known results. Finally, two illustrative examples are given to support the effectiveness and validity of the obtained theoretical results.

Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations

Abstract This manuscript concerns quasi-pinning synchronization and β-exponential pinning stabilization for a class of fractional order BAM neural networks with time-varying delays and discontinuous neuron activations (FBAMNNDDAs). Firstly, under the framework of Filippov solution and fractional-order differential inclusions analysis for the initial value problem of FBAMNNDDAs is presented. Secondly, two kinds of novel pinning controllers according to pinning control technique are designed. By means of fractional order Lyapunov method and designed pinning control strategy, the sufficient criteria is given first to ensure the quasi-synchronization for the dynamic behavior of FBAMNNDDAs. Furthermore, the error bound of pinning synchronization is explicitly evaluated. Thirdly, via Kakutani s fixed point theorem of set-valued map analysis, Razumikhin condition, and a nonlinear pinning controller, the existence and β-exponential stabilization of FBAMNNDDAs equilibrium point is obtained in the voice of linear matrix inequality (LMI) technique. Fourthly, based on as well as Mittag-Leffler function and growth condition, the global existence of a solution in the Filippov sense of such system is guaranteed with detailed proof. At last, a numerical example with computer simulations are performed to illustrate the effectiveness of proposed theoretical consequences.

Pinning Synchronization of Complex Dynamical Networks With Multiweights

In this paper, we introduce two complex dynamical networks with multiweights, which have several different sorts of weights between two nodes. By means of Lyapunov functional method and pinning control technique, some sufficient conditions are derived to ensure the synchronization for proposed network models. Moreover, some adaptive strategies are given to acquire suitable coupling strengths and feedback gains. By exploiting these designed adaptive laws, several general criteria for network synchronization are established. Finally, two numerical examples are also provided to show the validity of the theoretical results.

Distributed Adaptive Tracking Synchronization for Coupled Reaction-Diffusion Neural Network.

This paper considers the tracking synchronization problem for a class of coupled reaction-diffusion neural networks (CRDNNs) with undirected topology. For the case where the tracking trajectory has identical individual dynamic as that of the network nodes, the edge-based and vertex-based adaptive strategies on coupling strengths as well as adaptive controllers, which demand merely the local neighbor information, are proposed to synchronize the CRDNNs to the tracking trajectory. To reduce the control costs, an adaptive pinning control technique is employed. For the case where the tracking trajectory has different individual dynamic from that of the network nodes, the vertex-based adaptive strategy is proposed to drive the synchronization error to a relatively small area, which is adjustable according to the parameters of the adaptive strategy. This kind of adaptive design can enhance the robustness of the network against the external disturbance posed on the tracking trajectory. The obtained theoretical results are verified by two representative examples.

Exponential synchronization of Markovian jump complex dynamical networks with partially uncertain transition rates and stochastic disturbances

Abstract This paper studies the problem of exponential synchronization for a class of Markovian jump complex dynamical networks (MJCDNs) with stochastic disturbances and partially uncertain transition. By constructing the novel stochastic Lyapunov–Krasovskii function (LKF), and utilizing stochastic analysis, feedback pinning control technique and inequality techniques, some sufficient criteria are established in terms of linear matrix inequalities (LMIs) to guarantee the exponential synchronization of the MJCDNs with time delays and without it. Finally, according to a Markovian chain with partially uncertain transition rates, some numerical examples are given to demonstrate the effectiveness of the proposed results.

Synchronization for coupled reaction-diffusion neural networks with and without multiple time-varying delays via pinning-control

The synchronization problem for two types of coupled reaction-diffusion neural networks (CRDNNs) with and without time-varying delays is considered in the article. By utilizing pinning control technique and choosing appropriate Lyapunov functionals, we analyze synchronization of these network models. Firstly, by using some inequality techniques, a synchronization criterion is derived for CRDNNs. Secondly, in order to obtain appropriate coupling strength, an adaptive strategy is also developed. Furthermore, we generalize these results to the model of CRDNNs with multiple time-varying delays. Two illustrate examples including numerical simulations are presented to indicate the correctness of our results.

Passivity and Pinning Passivity of Coupled Delayed Reaction–Diffusion Neural Networks with Dirichlet Boundary Conditions

This paper respectively considers passivity problem and pinning passivity problem for coupled delayed reaction---diffusion neural networks (CDRDNNs). By construction of appropriate Lyapunov functionals and utilization of inequality techniques, several passivity conditions are derived for the CDRDNNs. Moreover, the pinning control technique is developed to obtain some passivity criteria for CDRDNNs. Finally, two numerical examples are also provided to verify the correctness of the theoretical results.

Pinning Control for Synchronization of Coupled Reaction-Diffusion Neural Networks With Directed Topologies

This paper proposes a directed complex dynamical network consisting of ${N}$ linearly and diffusively coupled identical reaction-diffusion neural networks. Based on the Lyapunov functional method and the pinning control technique, some sufficient conditions are obtained to guarantee the synchronization of the proposed network model. In addition, an adaptive strategy is proposed to obtain appropriate coupling strength for achieving network synchronization. Furthermore, the pinning adaptive synchronization problem is also investigated in this paper, and a general criterion for ensuring network synchronization is established. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.